in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

in this paper, an iterative scheme for extracting approximate solutions of two dimensional volterra-fredholm integral equations is proposed. considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. several examples are provided to demonstrate the effc...

A nonlocal boundary value problem for a system of
 hyperbolic equations of second order with generalized integral
 condition is considered. By method introduction functional
 parameters the investigated transformed to inverse
 unknown
 and additional functional relations. Algorithms finding solution inverse are constructed, their convergence is
 proved. The conditi...

The ADM Hamiltonian formulation of general relativity with prescribed lapse and shift is a weakly hyperbolic system of partial differential equations. In general weakly hyperbolic systems are not mathematically well posed. For well posedness, the theory should be reformulated so that the complete system, evolution equations plus gauge conditions, is (at least) strongly hyperbolic. Traditionally...

This work is devoted to study the existence and uniqueness of solution an analogue Gellerstedt problem with nonlocal assumptions on boundary integral gluing conditions for parabolic-hyperbolic type equation nonlinear terms Gerasimov–Caputo operator differentiation. Using method energy, have been proved. Existence was proved by successive approximations factorial law Volterra equations.

In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular propertie...